C Introduction. History of Coastal Inundation Models

Transcription

1 PAPER History of Coastal Inundation Models AUTHORS William G. Massey Jeffrey W. Gangai Elena Drei-Horgan Kevin J. Slover Dewberry C Introduction oastal storms and flooding are a normal occurrence in the coastal regions of the world and many instances of these have been recorded by historians, writers and mariners through the ages. Christopher Columbus reported one of these events after he sailed into a hurricane during one of his four voyages to the New World and lost lives and property. Hurricanes, tsunamis, Nor easters, and winter storms cause inundation of coastal and estuarine areas and, with the ever-increasing growth and development of coastal regions, greater loss of life and property damage will continue to occur on an even larger scale. Current damages caused by coastal flooding events worldwide have been measured in the billions of dollars, and thousands of lives have been lost. In order to co-exist with nature s destructive forces in these vulnerable areas, models are needed to predict the height, inland extent of flooding and destructive forces that could be produced by storms. One method to achieve this is the development and use of mathematical models that allow these storm systems to be simulated on a computer so their potential effects can be known. With the ability to predict inundation areas and depths, communities can require safer construction, lives can be saved, and property can be protected when future storms strike. The purpose of this paper is to provide a brief history of the use of coastal inundation models, highlighting their function and application as forecasting, planning, warning and monitoring tools while detailing their development chronologically. ABSTRACT Hurricanes, Nor easters, winter storms and tsunamis cause damaging and destructive inundation of coastal areas. With the rapid growth and development of coastal regions, greater damage to property and loss of life will continue to occur. The development and implementation of numerical models allows these natural events to be replicated so that their potential effect can be known and lives and property protected. A wide variety of models have been developed over the past forty years to forecast coastal inundation. The models described herein were chosen based on their use in emergency management and hazard mitigation. Although a brief overview of the numerical characteristics of each model will be provided, the paper aims to highlight their function and application as forecasting, planning, warning and monitoring tools while detailing the chronological development of coastal inundation models. Impact on Coastal Economy and Loss of Life and Property as a Result of Coastal Inundation Every year, coastal storms cause a tremendous amount of damage and loss of life in the United States. In the last ten years, more than 50 tropical storms and hurricanes made landfall along the U.S. coast, and many experts have predicted that this period of increased hurricane activity will continue for several more years. Nor easters are an annual threat to the eastern coastal portion of the country and cause hurricane-like damages over a wide area of the coast. Even though tsunamis are not considered a major threat by most of the population, National Weather Service experts are aware of the major threat they also pose to the United States. The damages and impact on the Gulf Coast caused by Hurricanes Katrina and Rita in 2005 are well documented and ranged in the billions of dollars. It will be decades before the Gulf region returns to its previous state of normalcy assuming additional storms do not occur in the area. The tsunami threat to the United States has not been assessed in the same manner and scale as coastal storms, but efforts are now underway to get a better assessment of the magnitude of that threat. After the 2004 Banda Aceh tsunami disaster in the Indian Ocean, Congress appropriated more than $26 million to expand the U.S. Tsunami Warning System (see Bernard and Titov, 2007). Hurricanes The origins of empirical models to forecast maximum storm-surge heights can be traced back to the mid-to-late 1950s. Conner et al. (1957) sought to provide forecast centers with an empirical procedure to provide an estimation of an extreme tide to be expected from a hurricane. Previous studies by Harris et al. (1963) were among the first to recognize the individual components affecting surges, though they failed to produce empirical procedures to quantify water levels. Conner et al. (1957) describe a methodology to quantify storm tide elevations using only the pressure difference between a storm s minimum central pressure and the ambient pressure. The maximum wind of a tropical cyclone is dominated by the cyclostrophic effect and computed by taking the square root of the pressure difference and multiplying by a constant, where the constant refers to the tightness of the pressure gradient. With a computed wind speed, it is possible to compute the wind stress over the surface of the ocean and the total setup from a tropical cyclone. Using historical observed data from Gulf of Mexico land-falling tropical cyclone events, they derived two equations. The first combines the maximum winds from the cyclostrophic effect and the total setup as computed by Montgomery (1955) to derive the following where h max is the maximum height 7

2 of the storm surge, 1005 is the pressure at the edge of the storm (mb), and p o is the pressure at the center of the storm: h max = 0.867(105 p 0 ) (1) Conner et al. (1957) improved Equation 1 by combining it with a wind stress equation to derive a regression equation for estimating surge elevations assuming the ambient pressure to be 1019 mb (Figure 1). Analyzing the same data set from the Gulf of Mexico, the second equation is as follows: h max = 0.154(1019 p 0 ) (2) FIGURE 1 The authors concluded that this incorporates only the basics of storm-surge forecasting. They note that pressure differences account for only about half of the total variability of storm-surge height along the open coast. The other parameters could not be properly described by the methodology presented. An important note is that this methodology is only valid for storms in the Gulf of Mexico. The simple reason is that if a storm enters the Gulf, then it must make landfall. Storms that move along the Atlantic Coast may make landfall, though only the circulation center may move over land, while the bulk of the storm remains over water. Later, Hoover (1957) concluded that equation 2 underestimates the maximum tide height because the maximum surge height is usually not observed. Both Hoover (1957) and Conner et al. (1957) assume that the dominating force producing storm surge is the minimum central pressure of the storm. Maximum tide or storm-surge height (h max ) on the open coast as a function of central pressure (p o ). Red squares represent observed surge elevations where the height of the surge and central pressure of the storm are known. The blue line represents Equation 1. The green line represents equation 2 (from Conner et al., 1957). However, Conner et al. (1957) assume that there is one point along the coast where the highest surge occurs and that surge height decreases with distance from this point. The resulting surge profile would be a symmetrical, bell shaped curve as others prior to him have noted. However, using historical data from the Atlantic Coast and Gulf of Mexico, Hoover (1957) plotted the profiles of each storm and noticed a common theme. Storms that made landfall on similar coastlines showed similar profiles. That is to say, storms that made landfall in New England had their maximum observed surge heights further from the center, on average, then those that made landfall along the Southern-Atlantic States (North Carolina, South Carolina, Georgia). Taking historical storms that made landfall north of Jacksonville, FL, for which the central pressures and tide data could be found, Hoover plotted these in a similar fashion as Figure 1. A correction was made for the maximum surge height dependent on the distance from the center of the storm, and the estimated maximum surge was plotted. As an example, consider a hurricane making landfall at Hilton Head, S.C. on August 28, 1911 with a maximum observed tide of 5.6 feet above normal and a minimum central pressure of 981 mb. Hoover estimated that the maximum tide level occurred 30 miles to the right of landfall with a maximum tide of 8.0 feet above normal compared to 5.6 feet using the bell curve of Connor et al. As computed by Hoover, the regression to estimate maximum surge heights (h ext ) along the Atlantic Coast is as follows: h ext = 0.198(1006 p 0 ) (3) Hoover computed a new regression line for the Gulf of Mexico as well, using the same methodology he used for the Atlantic Coast as follows: h ext = 0.151(1032 p 0 ) (4) It was noted by Hoover that the difference in the ambient pressures between equations (2) and (4) (1019 and 1032, respectively) was a result of the assumption made by Conner et al. (1957) that the actual extreme 8 Marine Technology Society Journal

3 tide is higher than the maximum observed tide. Hoover also noted that the variance between the proportionality constants (0.154 and 0.151, respectively), though slightly different, is insignificant. Harris (1963) introduced a more complex methodology for predicting storm-surge heights. Recognizing the complexity of surge forecasting, he developed a computer-aided empirical model that included five separate processes associated with storm-surge forcing as follows: a. Pressure Effect: Also called the inverse barometer effect, this is a result of the lower pressure of the storm causing the water to be displaced upward. The rule of thumb is for every 1 mb drop in pressure there is a 1 cm rise in ocean surface. b. Direct wind effect: In shallower waters along the East Coast, wind-driven currents tend be in the same direction of the wind and, for north-south winds are guided by depth contours. The forcing of the water towards the coast by onshore winds causes a build-up of water along the shoreline and is generally referred to as wind set-up. Offshore winds have the reverse effect. c. Coriolis Force: As a result of the rotation of the earth, wind-driven currents in the Northern Hemisphere are deflected to the right in a rotating frame of reference. Thus, winds with a north-south component along the East Coast cause an increase in sea level along the coastline when the coast is to the right of the wind flow and a decrease in sea level when the coast is to the left of the direction of the wind. d. Waves: Wind-induced waves generally travel in the direction of the wind. Breaking waves along the shore have a considerable amount of momentum associated with them, allowing them to travel further onshore then the mean water line. The result of this may be the overtopping of berms and ponding of water in low-lying areas behind the berms. In addition to overtopping, wave set-up during more powerful events can cause an increase in water level elevations near shore. As the wave breaks onshore and retreats seaward, its progress may be impeded by the next wave. This will eventually induce a sealevel rise near shore. e. Rainfall: Large amounts of rain and inland flooding are generally associated with major tropical cyclones. As the rains run off into river basins and flow seaward, this will induce a rise in sea level at the mouth of these rivers. The increased heights at the mouth can eliminate or reverse the normal gradient in river levels, causing a buildup of water higher then average. Harris s first approximation demonstrated that the effects of the Coriolis force, waves, and wind set-up at sea are all proportional to the wind stress, and that the wind stress is proportional to the pressure gradient (assuming a geostrophic wind). Harris further observes that, in general, rainfall is correlated with below-normal pressures, resulting in all five factors being directly related to pressure gradients. Summary of Common Coastal Inundation Models The complexity of processes that cause coastal flooding and the need for tools to identify, evaluate, and predict the risk of floods in coastal areas has attracted researchers worldwide. Today there are a large variety of coastal inundation models that are being used to simulate and forecast hurricanes, Nor easters, and tsunamis and their impacts. Because of this broad spectrum of models this paper will focus on those, mainly government sponsored, that are currently used for emergency management and hazard mitigation. Special Program to List Amplitudes of Surges from Hurricanes SPLASH During the 1960s, Jelesnianski et al. (1972) continued to improve on empirical models discussed previously. Advances in computing power during this time allowed for more complex equations and additional parameters to be included, eventually leading to an off-the-shelf computer program called SPLASH. The first necessary output required is the predicted maximum surge potential based on the empirical formulas derived by Conner et al. (1957) and Harris (1963). The initial calculation is made to determine the maximum surge given the following constraints: 1. There are sets of storms, and in each set, the radius of maximum winds (R) is held constant. 2. In each set of storms, only the pressure drop ( P) is varied. 3. All storms have standard motions (a storm motion with a speed of 15 miles per hour and a track normal to the coast, from sea to land; the storm must move onto land). 4. All storms traverse a standard basin (a standard basin is a basin with a straight line coast in which the depth profile is a linearslope). 5. All storms make landfall at 30 N. The resulting nomogram from this first model allows the forecaster with a known P and R to calculate a crude maximum surge. Several interesting results occurred when examining this first calculation. First, it was helpful in demonstrating the sensitivity of the calculation of P. A 1 millibar error for a pressure drop of 100 millibars gives a storm-surge calculation error of 1%. Second, with P held constant, peak surges were observed to be at their absolute maximum at around R = 30 miles. The second calculation was to correct the maximum surge for near coastal bathymetry. Again, using a computer model, the following constraints were used (for both the Gulf Coast and East Coast): 1. Each storm has its own variant in P and R. 2. Both storms (i.e., Gulf Coast and East Coast) have the same standard motion. With these constraints and the varying sea depths, a shoaling factor was computed along both the Gulf Coast and East Coast. It was discovered that the shoaling factor was proportional to the distance of the 10 fathom curve from the shoreline (i.e., the further away the 10 fathom curve from the coast, the higher the shoaling factor and the greater the surge potential). Selected cities along both coasts were chosen based on location and proximity to each other (ultimately, reference points were identified approximately every 100 miles), and shoaling factors were computed at these stations. The third and final calculation was to correct for the storm direction. In all empirical models until this time, it was implied that all storms struck the coastline in a perpendicular fashion. The third calculation accounted for the storm s actual movement. Again, constraints were necessary to simplify this calculation: 9

4 1. All storms have an R = 22.5 miles and a P = 62 mb. 2. All storms transverse a standard basin. The results allowed the forecaster, with a known storm direction and forward speed to calculate the ratio of the generated peak surge to that generated by a storm with standard motion. With the three variables computed, the maximum expected surge can now be computed for a land-falling hurricane. The input parameters are now as follows: R : radius of maximum winds in miles, 10 < R < 50 MPR : miles + R, distance from peak surge from a reference station P OO : mean ambient pressure about the storm P O : central pressure of the storm P : P OO - P O ; the pressure drop from the storm U S : speed of storm on shelf θ : angle from coast to storm track And the equations are as follows: SS = S P F G F M (Gulf Coast) SS = S P F E F M (East Coast) Where: S P = preliminary maximum surge value F G and F E = correction factor for shoaling for the Gulf and East coasts, respectively F M = correction factor for vector storm motion Tetra Tech (FEMA SURGE Model) The FEMA SURGE model was first introduced in 1976 in response to a recommendation by the National Academy of Science (NAS) in 1975 (Camp Dresser et al., 1985). At this time the FEMA surge model was known as TTSURGE because it was developed by Tetra Tech, Inc. After the Federal Insurance Agency (FIA) became know as FEMA, after extensive use by FEMA for application in Flood Insurance Studies (FIS), and after several model updates initiated by FEMA, the surge model became known as the FEMA SURGE Model. TTSURGE provided the flood elevations and was used to map the coastal inundation hazards on Flood Insurance Rate Maps (FIRMs) in the late 1970s. In the early 1970s, FEMA used NOAA tide gauge statistics to obtain the flood elevations used on these FIRMs The FEMA TTSURGE model uses an explicit, two-dimensional (2D), space-averaged, finite-difference scheme to simulate the surges caused by hurricanes. Inputs to the model include the bathymetry, coastline configuration, boundary conditions, bottom friction, and other flow resistance coefficients. Also required are the surface wind stress and atmospheric pressure distributions of a hurricane. The model is separated into two parts, the hurricane storm model and the hydrodynamic model. In the hurricane storm model the hurricane is described by its barometric pressure field at sea level and the corresponding wind field over the sea surface. These two fields are parameterized by the radius of maximum winds and the central pressure depression. These parameters are used to define the wind speed and barometric pressure gradient distributions radially about the eye of the storm. The location of the eye of the storm as it moves forward and its translational velocity are used in turn to describe the complete history of the barometric field and wind field everywhere on the hydrodynamic grid. The stress produced by the wind and barometric pressure gradients provide the force for the hydrodynamic model. The wind and pressure distributions are based on data observed from hurricanes. The hydrodynamic model uses the principles of conservation of momentum and mass to simulate the water surface response to hurricanes. The model uses a rectangular grid to represent the area of interest and usually employs a nested grid system so that greater detail can be added along the coastline. A Manning s n (coefficient of roughness) and ground elevation are specified at the center of each cell of the grid and the water surface elevations are calculated at the center of each cell. The FEMA surge model results are used to perform a Joint Probability Method analysis to determine the return periods of surge elevations, unlike the Sea, Lake and Overland Surges from Hurricanes (SLOSH) model, which typically is based on the category rating of a storm based on wind speed (see below). In 1983 the NAS published a report (NAS, 1983) evaluating the FEMA TTSURGE model and made a number of recommendations for improvements. FEMA tasked Camp Dresser & McKee Inc. (Camp Dresser et al., 1985) to incorporate the recommended changes to the model. The changes were based on advances in technology and experience acquired during past FEMA Flood Insurance Studies. The changes to the model included modifications to the following: wind model, wind stress formulation, friction term, treatment of bottom friction in inland areas, treatment of barrier islands, and coarse grid and nested grid interfaced at their boundaries. These changes to the model were completed in 1985, and a new version of the model was released. After the significant changes to the surge model performed by Camp Dresser & McKee Inc., the FEMA TTSURGE model became known as the FEMA SURGE model. In 1988 FEMA identified a need for additional updates to the surge model; these changes were performed by Greenhorne & O Mara, Inc (FEMA, 1988). The barrier inlet channel routine was heavily modified. The hurricane storm model was adjusted to reflect current information on wind-stress coefficients and the radius-to-maximum winds formulation. The late 1980s was the last time the FEMA SURGE model was used in a new or updated flood insurance study to revise the FIRMs. In the early 1990s coastal engineering firms were updating the model to run on desktop PCs and updated Fortran compilers. The model was also revised to include variable inflow hydrographs. Since this time, the model has not been updated to include any recent changes in technology for use in a flood study. FEMA also had a surge analysis and model developed specifically for the mainstream of Chesapeake Bay (not including its tributaries). The model was developed in 1978 by the Virginia Institute of Marine Science (FIA, 1978). Unlike the FEMA SURGE model, this model used a two-dimensional finite element grid 10 Marine Technology Society Journal

5 scheme. The analysis considered both extratropical storms and tropical storms. The two types of storms were treated as statistically independent. The extra-tropical storms were analyzed by using six tide stations around Chesapeake Bay. For tropical storms, a storm-surge model was developed. The maximum surgefrequency curves from extra-tropical and tropical storms were then statistically combined. SLOSH Sea, Lake, and Overland Surges from Hurricanes Developed by the Techniques Development Laboratory of the National Weather Service, the SLOSH model (Jelesnianski et al., 1992) is a two-dimensional, numerical-dynamical tropical storm-surge model developed for real-time forecasting of hurricane storm surges. The SLOSH model is currently the only model used by the National Hurricane Center to provide real-time storm-surge guidance. At its inception, only curvilinear, polar coordinate grid schemes were used, but recent changes to the model have introduced elliptical and hyperbolic grids, allowing a finer resolution cell size near shore and a coarser cell size over areas of less importance. FIGURE 2 Each grid cell contains a number of elements for determining whether it will remain dry (not inundated) or wet (inundated) that are assigned prior to running the model. For each cell, the elevation or depth must be assigned in similar vertical datums, and surface wind coefficients must be determined and assigned based on the topography of the land. For inland grid cells, the surface wind coefficient can be either a lake wind without trees or a lake wind with trees. For grid cells over water, the coefficients become either lake wind without trees or ocean wind. Sub-grid elements such as two-dimensional barriers (dunes, levees, and elevated roads), channels and cuts are represented in the model as well. Once the basin is populated, the model is applied to both hypothetical storms to create Maximum Envelopes of Water (MEOW) and Maximum of MEOWs (MOMs) and to provide real-time forecasts. The MEOW is the maximum surge elevation at every grid cell that is reached in any of several envelopes, where the envelopes are acquired by running the model on storms with the same category, forward speed, and direction of motion, but with tracks that are parallel to each other. A Maximum forecasted surge heights for Hurricane Rita from SLOSH operational run, based on Advisory Number 21 from the National Hurricane Center. MOM is the maximum surge elevation at every grid cell that is reached in any of several MEOWs, where the only constant is category. For real-time forecasting purposes, the inputs to the model remained simple. The forecaster only needs to know the current position and forecasted track, size (radius of maximum winds), and intensity (P). Once entered, the SLOSH model computes the wind fields associated with this storm based from the DP. Once wind fields are generated, the model computes on a cell by-cell basis the wind stress, which is the underlying force for creation of storm surge. An example of a SLOSH basin and surge results are shown in Figure 2. Advanced Circulation Model - ADCIRC The Advanced Circulation Model (ADCIRC) was developed as a joint project between the USACE Engineering Research and Development Center, University of Notre Dame, and University of North Carolina Chapel Hill (Luettich et al., 1992). ADCIRC is a highly developed computer program for solving the equations of motion for a moving fluid on a rotating earth. These equations have been formulated using the traditional hydrostatic pressure and Boussinesq approximations and have been discretized in space using the finite element (FE) method and in time using the finite difference (FD) method, which allows for a highly flexible, unstructured grid. ADCIRC can be run either as a two-dimensional depth-integrated (2DDI) model or as a three-dimensional (3D) model. In either case, elevation is obtained from the solution of the depth-integrated continuity equation in Generalized Wave-Continuity Equation (GWCE) form. Velocity is obtained from the solution of either the 2DDI or 3D momentum equations. All non-linear terms have been retained in these equations. ADCIRC requires input of wind and pressure fields to simulate hurricanes. These wind and pressure fields are developed by meteorological models independent of the ADCIRC model. ADCIRC simulates tidal circulation and storm-surge propagation over large computational domains, eliminating the need for imposing approximate open-water boundary conditions near the area of interest that can 11

6 create inaccuracies in model results while simultaneously providing high resolution in areas of complex shoreline and bathymetry where it is needed to maximize simulation accuracy. The targeted areas for ADCIRC application include continental shelves, nearshore coastal areas, inlets, and estuaries. Typical ADCIRC applications have included modeling tides and wind-driven circulation, analysis of hurricane storm surge and flooding, dredging feasibility and material disposal studies, larval transport studies, and near-shore marine operations. An example of a coarse Atlantic, Gulf, and Caribbean grid is shown in Figure 3. Features available in ADCIRC include: wetting/drying of low-lying areas, overflow and throughflow barriers, bridge piers, wave radiation stresses, sediment transport, and morphology change. Planned enhancements include modeling salinity, contaminant transport, threedimensional (3D) sediment transport/morphology change modeling, and additional sediment transport algorithms. The model can be run as a single processor code or in parallel mode running efficiently on hundreds of processors. ADCIRC includes message passing interface (MPI) library calls to allow it to operate at high efficiency (typically better than 90 percent) on parallel computer architectures. FIGURE 3 East Coast 2001 Tidal Database ADCIRC Domain, USACE. ADCIRC can be run with many boundary conditions, including: elevation boundary conditions, normal flow boundary conditions, surface stress boundary conditions, and tidal potential with earth load/self attraction tide. ADCIRC can be forced with surface stress (wind and/or wave radiation stress) and atmospheric pressure. ADCIRC was first developed in the early 1990s and was primarily used by the USACE. The USACE needed for a tide and circulation model in order to simulate real conditions to evaluate the impact of USACE s projects and to evaluate alternative project designs. The USACE used ADCIRC for small-scale projects, including navigation and channel design, dredging, and design of flood and storm damage reduction projects. In the late 1990s the USACE and the model developers teamed with Brigham Young University and Environmental Modeling Systems, Inc. (EMS-I) to create a Windows user interface called the Surface Water Modeling System (SMS) to support ADCIRC model setup and mesh generation as well as post-processing tools to view the model results. Previous to this, ADCIRC was run and set up using text files which made model setup and mesh creation very time consuming. At this time, the Windows interface SMS and ADCIRC became publicly available for purchase through EMS-I. After the year 2000, the USACE started using ADCIRC for water-quality studies and larger scale surge-prediction studies. At this time, the user base was expanding but the model was still primarily used by USACE for navigation and storm protection projects. ADCIRC was still difficult to run at larger scales due to the computing power needed, making it necessary to run on larger super computers. As the desktop computer s processing speeds advanced, it became more economical and easier for general users to have access and run ADCIRC at larger regional scales. In 2002, ADCIRC was accepted by FEMA to predict return periods of storm surges for use in Flood Insurance Studies (FIS). In this capacity ADCIRC would be used to define the inland limit of flooding and as a base to calculate wave heights for mapping coastal hazards on FEMA s Flood Insurance Rate Maps (FIRMs). Two of the first studies using ADCIRC to make its way onto the FIRMs were for the island of Rota and the American Samoa islands in the Pacific. Both of these studies were performed by USACE for FEMA. The first private firm to apply ADCIRC for a FEMA FIS was done for the U.S. Virgin Islands and Puerto Rico (FEMA Region II). Previous to these studies, the last time surge modeling was updated for a FIS was in the late 1980s using the previously described FEMA surge model. In the 1990s USACE developed ADCIRC for use with sediment transport and morphology change studies, particularly around inlets. ADCIRC can also now be coupled with 2D wave models to add the wave radiation stress or wave setup component to the ADCIRC surge model. ADCIRC is also being used to develop downstream tidal boundary conditions for input to riverine models for predicted flooding along rivers. Many universities have recently adopted the use of ADCIRC for performing surge and wave flood inundation level forecasting from approaching storms. These forecasts are based on the National Weather Service reports of the storm characteristics and use a relatively coarse mesh in order to run the forecast quickly. Universities such as the University of Florida 12 Marine Technology Society Journal

7 and the University of North Carolina (Luettich et al., 2005) have working models set up for the states of Florida and North Carolina, respectively. The university forecasts are not meant to replace the official forecasts and warnings made by NOAA and the National Weather Service but are used for research and supplemental data. The Oregon Graduate Institute has also modified ADCIRC for use in tsunami modeling and is applying it to develop inundation maps for Oregon. In the past five years, the National Oceanic and Atmospheric Administration (NOAA) has also used ADCIRC for tidal and sea-level rise studies. NOAA has been using ADCIRC to develop a local vertical datum conversion tool called VDatum ( gov/csdl/vdatum.htm). Currently ADCIRC is being applied to a number of FEMA flood studies, such as its use in Hawaii to update the FIRMs for FEMA. Previous flooding in Hawaii on the FIRMs was based on tsunami inundation, but there is a significant threat of hurricane flooding on the south side of the Hawaiian Islands. ADCIRC is also currently being applied for FEMA in Mississippi and Louisiana after the devastating effects of Hurricanes Katrina and Rita. These two events showed that the current FEMA FIRMs were under-predicting the flood elevations. Before the recent hurricanes, the ADCIRC modeling was being used by the USACE in Louisiana and in New Orleans for levee design. The strength of DYNLET is its capacity to predict elevation levels and velocities in a simple-to-create spatial environment (Cialone et al., 1993). Its primary use is to predict elevation and flow velocity to determine design levels, to perform storm simulations, to determine velocity exceedance curves, to determine the water surface dynamic between interconnected bays, and to model river networks. The model provides reliable and accurate answers while requiring minimal modeling expertise, data entry, and numerical grid generation. The model solves the full l-d shallow water equations, employing an implicit finite difference technique. The equations are applicable to tidal flow, flows in lakes and reservoirs, river flow, and wave motion where the wavelength is significantly greater than the water depth. The model resolves water elevations and velocities at nodes of a channel, where the term channel is used to identify any body of water that conveys a flow along its length, regardless of width. It is also able to provide solutions for a network of interconnecting channels such as those shown schematically in Figure 4. FIGURE 4 Complex system of networking channels (from Amein & Kraus 1991). Boundary conditions are provided, as known flow or surface elevation, at the external boundary (open ocean) and at junctions, as well as at internal boundary conditions at cross sections. This is to represent flow entering or leaving the system due to tributaries, precipitation, evaporation, and any other process that may alter the flow rate inside the studied system. Bottom shear stress through the implementation of Manning s formula, and surface shear stress generated by the wind are taken into consideration by the model. Two important features of this simple 1- D model are its capacity to (1) calculate the effect of submergence of bridge decks under high water, as well as culverts under low or high water conditions and (2) account for flow overtopping of barrier beaches by defining barrier islands as weirs. DYNLET is on the list of FEMA-accepted numerical models to perform coastal stormsurge studies. Specifically, DYNLET finds its special niche in the study of tidal flow along channels and inlets. For this purpose DYNLET has been applied in several studies by USACE. One example is the study of the One-Dimensional Model of the Dynamic Behavior of Tidal Flow at Inlet - DYNLET DYNLET is a one-dimensional (1-D), numerical model developed by Amein and Kraus (1991) under contract to the U.S. Army Corp of Engineers Waterways Experiment Station (WES) and Coastal Engineering Research Center (CERC). The model predicts tide-dominated velocities and water levels for fluid flowing from the ocean through a tidal inlet, back-bay regions, and up tributaries. Because of these properties, DYNLET has been used to push surge upstream, making it an easy-to-use surge model. In addition, it accurately represents the flow distribution across any cross section. 13

8 Chowan River Estuary in North Carolina. The goal of the study was to evaluate the water surface elevation, velocity, and discharge at the crosssection of the U.S. Route 17 bridge for the 5-, 10-, 50-, 100-, and 500-year flood in order to identify the best hydraulic solution for the design of a new proposed bridge 30 meters south of the existing one. For this study, storm-surge levels were determined from two sets of storm parameters and historical surge data from tidal gauges, recorded during Hurricanes Hazel (1954) and Diane (1955), and used to develop tidal elevation at different return periods. The combined surge and tide elevations were then used in the computations to evaluate different design alternatives. DYNLET has been recently applied to the study of water-surface elevation and current velocity at Goldsmith Inlet and Goldsmith Pond, Long Island, N.Y., as part of a broad and detailed study of the geomorphic analysis of the Mattituck Inlet (Morgan et al., 2005). Because Goldsmith Inlet is a system in which the flow is primarily directed along the channel, DYNLET works well because it is a simple and less time-consuming model. The model was driven by water-level measurements obtained off Mattituck Inlet and calibrated using bottom friction coefficients based on the particular sediments present in the Goldsmith channel. The model results fit both field elevations and velocity well and helped provide a clear understanding of the relation between the geomorphology of the inlet and the flow behavior. MIKE 21 2D Modeling System for Floodplains The DHI Water and Environment (DHI) MIKE 21 system can predict currents and water levels through the application of hydrodynamic and wave modules. The MIKE 21 hydrodynamic Flowmodel (DHI, 2005a) is the central module responsible for determining water surface elevation due to astronomical tide, wind stress, and barometric pressure gradients in environments such as the Great Lakes, estuaries, nearshore areas, and rivers. The model exists in a rectangular grid finite difference version (which can also include dynamically nested rectangular sub grids), and a flexible triangular mesh, finite volume version, allowing for variable resolution throughout the model domain. The model solves the full time-dependent, nonlinear, depth-averaged equations of continuity and conservation of momentum. Simulations of water level fluctuations and flows can be run for a broad variety of forcing. Wind and pressure fields can be directly fed to the model or determined using one of two MIKE 21 wind-generating programs. The rectangular grid version is currently approved for FEMA usage on National Flood Insurance Program (NFIP) studies. Wave mechanisms can be taken into account by various wave modules included in the MIKE 21 system. Two of the models are briefly described here. The MIKE 21 Spectral Wave Flexible Mesh (SW FM) (DHI, 2005b) is a flexible mesh spectral wind-wave model for describing the propagation, growth and decay of shortperiod waves offshore and nearshore. It takes into consideration the effects of refraction, shoaling, wave generation due to wind, energy dissipation due to bottom friction, and wave breaking. The module also calculates radiation stresses that can be directly inputted into the flexible mesh hydrodynamic Flowmodel. This allows a continuous exchange, at every time step, of currents, water levels, and radiation stresses back and forth between the two modules. Alternatively, the radiation stresses can be included as transfer boundary conditions (decoupled) to the finite difference rectangular grid Flowmodel. The MIKE 21 FM SW model is approved for FEMA use on NFIP studies. The Nearshore Spectral Wind-Wave (NSW) module (DHI, 2005c) is a spectral wind-wave model that describes the propagation, growth, and decay of nearshore shortperiod waves. It can resolve refraction, shoaling, wave generation due to wind, energy dissipation due to bottom friction and wave breaking. The computed radiation stresses can also be inputted into the FLOOD module. The MIKE 21 NSW model is approved for FEMA use on NFIP studies. Other wave modules in the DHI suite include the MIKE 21 PMS (Parabolic Mild Slope) and MIKE 21 BW (Boussinesq Wave) model. These modules are not included on FEMA s approved model list but are very useful for applications where diffraction and wave setup is a critical component. The MIKE 21 modeling system is a world-renowned modeling system. In the United States it has been used in conjunction with projects of USACE, FEMA, the U.S. Bureau of Reclamation, and the National Aeronautics and Space Administration (NASA). Numerous MIKE 21 modules are included on the list of accepted models used by FEMA for the NFIP: As a test case, in 1999 the MIKE 21 system was used to determine flood levels for NASA at the Kennedy Space Center in Cape Canaveral, FL. The study predicted hurricane storm-surge levels for the coastal areas surrounding Cape Canaveral, including inlets and inland waterways. To determine total water level, the processes evaluated during the passage of a hurricane included: astronomical tide, storm-surge generated by wind stress and atmospheric pressure variations, wave set-up, and overland propagation of wind-generated waves. The stormsurge contributions from the tide, wind, and barometric pressure were determined from the MIKE 21 Nested Hydrodynamic (NHD) numerical model. A total of five nested grids were used, ranging from 8,100- meter to 100-meter grid spacing. The MIKE 21 OSW (now known as MIKE 21 FM SW) model was used to determine the offshore wave conditions generated from the hurricane winds. The MIKE 21 OSW results were compared with nearshore buoy measurements during the historical hurricane event and calibrated accordingly. The wave setup contribution to the total water level was computed from the combination of the OSW and NHD model results. Overland wave conditions were obtained using a combination of numerical models, including MIKE 21 NHD, MIKE 21 OSW, and MIKE 21 NSW. MIKE 21 OSW provided offshore boundary wave conditions to the MIKE 21 NSW model. The MIKE 21 NHD stormsurge elevations were used to provide initial water surface elevations to the MIKE 21 NSW model. This study was completed in the spring of 2000 and has been approved by NASA officials (NASA, 2000). More recently (Kerper et al., 2006), the MIKE 21 system was used by FEMA as part 14 Marine Technology Society Journal

9 of a prototype study aiming to test the new FEMA Guidelines and Specifications for the Pacific Coast of the United States (FEMA, 2004) and is currently being applied to a FEMA coastal hazards analysis study in San Francisco Bay. Tsunamis A tsunami is trigged by a sudden vertical displacement of water mass due to mechanisms such as earthquakes, sub-marine and aerial mass failure, volcanic eruptions, and collapses of volcanic edifices (see Bernard and Titov, 2007). The entire water column is displaced and a train of long waves with small steepness travel the ocean as a ripple in a pond. In deep waters, a minor displacement (less than 1 meter) is generated at the water surface, making tsunamis difficult to identify. A single wave may have a wavelength up to 500 km with periods of the order of 10 minutes to 2 hours and travel the open ocean at a speed up to 950 km/h (as fast as a jet airplane). As the waves approach the coast and interact with shallow water, the reduction of the wave velocity induces a decrease of the wavelength and a consequent increase of the wave steepness. A tsunami s runup height depends on the slope of the coast, and it has been proven by Synolakis (2006) that the height is not correlated with the magnitude of the parent earthquake. Runup heights ranging from 5 m to 26 m occurred after the tsunami triggered by the 1992 Flores, Indonesia, earthquake; runup heights of 15 m were surveyed after the Papua New Guinea tsunami of 1998; extreme runup heights of 31 m were measured after the 1993 Hokkaido-Nansei-Oki, Japan. Although basic governing equations were known for more than a century (Russel described the shape of a solitary wave in 1845), the lack of field data for validation had, until the 1990s, limited the development of tsunami modeling. Although the catastrophic 1946 tsunami that hit Scotch Cap, Alaska and Hilo, Hawaii and the Great Chilean tsunami of 1960 brought to light the need to investigate tsunami generation and warning, over the 1950s and 1960s research concentrated on long waves on a sloping beach using both LSW and NSW equation, or tsunamis described as bores. At that time, tsunami arrival was only roughly estimated. The approached used by Houston and Garcia (1974) to describe tsunami propagation was groundbreaking for the time. They studied, applying more realistic initial conditions, the propagation of a far-field tsunami using both analytical and numerical methods developed to supplement historical data in determining the ten largest tsunami elevations from 1837 to In 1978 the numerical model was then adjusted and verified by comparing numerical calculations with tide gauge recordings of the Chilean tsunami of 1960 and the Alaska tsunami of The maximum inland inundation limit was then calculated using the method described in Bretschneider and Wybro (1976). These methods, even if they provided results that closely matched historical data at the time, had the limitation of not being able to accurately assess the inland runup elevations. From the standpoint of FEMA s NFIP, inland flooding due to tsunamis was taken into account and mapped for the areas of Hawaii (FEMA, 2004a) and the California coast. The effective FIRMs for those areas show a risk of tsunami flooding that relies on a methodology developed by Houston and Garcia (1974). In the 1990s, when tsunami inundation models improved, higher resolution bathymetry and topography became available, and large databases became available both for far-field and nearshore tsunamis. This resulted in the need for FEMA to identify a methodology that could update the guidelines on tsunami inundation mapping. That need found a solution in the newly developed MOST model that became available at the end of 1990s. The MOST (Method of Splitting Tsunami) model is the state-of-the art model adopted by NOAA for the simulation of tsunamis. It is currently used by the Center for Tsunami Inundation Mapping Efforts (TIME), part of the NOAA Center for Tsunami Research (NCTR), for the preparation of inundation maps and delineation of evacuation routes. The model can simulate the generation, propagation, and runup of earthquake-generated tsunamis. The generation process is based on the elastic fault plane model that uses the concept of static sea-floor deformation to calculate the initial conditions that allow the tsunami generation and propagation (Titov, 1997). In order to accurately represent the propagation of a tsunami wave, the earth s curvature, the Coriolis force and the dispersion processes are included in the non-linear shallow-water equations (Murty, 1984) on which the MOST propagation module is based. The inundation part, by far the hardest to simulate, is determined as the runup elevation on dry land. Gridded bathymetry and topographic data, with a horizontal resolution of m in the nearshore area, are essential for the calibration of the model, as well as high-quality field data. The MOST model was able to simulate the 1993 Hokkaido-Nansei-Oki tsunami (Titov and Synolakis, 1997) accurately as indicated by the close agreement with the field data. This suggests that, with the availability of high-quality terrain data, the MOST model is a good tool for real-time tsunami simulation and inland flooding prediction. On the occasion of the 2004 Sumatra Tsunami (Titov et al., 2005), the MOST model was used to interpret and study the worldwide tsunami propagation. The results were compared with both tide gauge records around the globe, satellite measurements and field data. The model demonstrated how the energy from a localized earthquake could propagate through the entire world ocean, with impacts and damages a consequence of morphological source focusing and impact of topography on wave propagation A pilot project, led by NOAA s U.S. National Tsunami Hazard Mitigation Program (NTHMP) in partnership with FEMA, the U.S. Geological Survey, the National Science Foundation, and the emergency management and geotechnical agencies of the five Pacific states (Wong et al., 2005), was developed to implement the new advances in tsunami hazard assessment. The study was performed for the community of Seaside, Oregon (Gonzalez et al., 2004). The project uses the probabilistic tsunami hazard analysis (PTHA) and attempts to model the magnitude of tsunami flooding from multiple sources (Geist and Parsons, 15

10 2005) in order to obtain elevations for the 1- and 0.2-percent annual probability events. The MOST model was used to study the generation, propagation and inundation of both far-field and nearshore tsunamis. The combination of inundation data with tidal data, by probabilistic tsunami hazard assessment calculations, provided a hazard curve that describes the probability of recurrence, at a certain location, of a tsunami flood exceeding a specified wave height (Mofjeld et al., 2005). The results obtained from the Tsunami Pilot Study Working Group were implemented in the FEMA Phase 1 Focus Study completed in Nor easters After the winter storm that hit New England in February 1978, the need became evident for a model capable of simulating flooding events generated by Nor easters (winter extratropical storms). Although several surge models existed at that time, no wind model to simulate Nor easters was available. Stone and Webster (1978) developed for the Federal Insurance Administration (FIA) an empirical model that could reproduce wind and pressure fields for Nor easters. The coupling of those parameters with a surge model allows a more accurate determination of flood elevations along the northeast coast of the United States in the path of winter storms. The model used meteorological parameters such as pressure and wind fields to reproduce those of historical Nor easters. Eight historical storms were selected from 100 recorded between 1959 and 1976 as a basis for the study. The synthetic pressure field was parameterized as a function of the radius of maximum wind, accounting for the asymmetrical nature of a Nor easter front. The simulated pressure field was then used to generate a synthetic wind field. The method of the equilibrium wind, which unlike the geostrophic wind accounts for the effects of storm motion and surface friction, was preferred. Once the synthetic pressure and wind fields were evaluated, the model was verified against four historical storms. These storms were selected according to the intensity of the associated flooding and availability of wind 16 Marine Technology Society Journal and surge data. Of these storms only one was part of the initial set of storms used to develop the wind and pressure fields. The results found close agreement between the predicted pressure and wind fields and observed ones, indicating that the synthetic model was capable of providing a reasonable approximation of real extratropical storms parameters. A case study in southern Maine was used to test the surge levels generated by the February 1972 storms by applying the synthetic wind and pressure fields to the Tetra Tech surge model, a coupling that has since been called the Synthetic Nor easter Model. Good agreement was found between simulated results and surveyed water levels, confirming the validity of synthetic generation of wind and pressure fields as input for a model capable of representing coastal surge caused by Nor easters. Since its development the Synthetic Nor easter Model has been used as the major source of determination of still-water elevations, for the FEMA Flood Insurance Studies (FISs), primarily for areas north of Boston, as well as a few areas along the New Jersey and Delaware coastlines. In 1980, USACE developed tidal flood profiles based on storm peaks measured at USACE and NOAA tidal gauges for the New England area and revised in them in 1988 (USACE, 1988). These tidal profiles have been used to update the storm-surge stillwater elevation (SWEL) in New England flood insurance studies since The Nor easter Model is being replaced by the USACE tidal profiles when new coastal flood studies are being performed for FEMA flood insurance studies. Future of Coastal Inundation Modeling FEMA and other state and regional entities utilize the SLOSH model as the planning basis for the hazards analysis portion of the Hurricane Evacuation Studies (HES) conducted for state and local governments. The National Hurricane Center uses the SLOSH model in an operational mode to forecast hurricane surge elevations in a real-time mode. FEMA uses the ADCIRC model in the development of the FIRMs for flood insurance purposes. USACE uses ADCIRC for navigation and storm protection projects. NOAA uses the ADCIRC model for tidal calibrations and incorporation into its vertical datum transformation software VDatum. NOAA has formed a working group to assess the current effectiveness and accuracy of the various storm-surge models as described in this article. The results of the group s work will be revealed in the next several years. These results will forge a path into the future to develop a new, multipurpose model that will be used for real-time forecasts, hurricane evacuations studies, and FEMA s FIRMs. There continues to be a great need for models that are fast enough to be used in realtime and have the resolution needed for use in HES and FIRMs as well as other inundation studies. Acknowledgments The authors would like to thank Mr. Dale R. Kerper, DHI Water & Environment, Inc., San Diego, for providing reference materials regarding DHI software and case studies and Mr. Jeff Sample, Dewberry, for providing documentation on tidal profile studies for the New England area and on historic FEMA surge modeling. References Amein, M. and Kraus, N.C DYNLET1: Dynamic Implicit Numerical Model of One-Dimensional Tidal Flow through Inlets. Technical Report CERC 91-10, U.S. Army Engineer Waterways Experiment Station, Coastal Engineering Research Center, Vicksburg, MS. Bernard, E. and Titov, V.V Improving tsunami forecast skill using deep ocean observations. Mar Technol Soc J. 40(4): Bretschneider, C.L. and Wybro, P.G Tsunami Inundation Prediction. 15 th International Conference on Coastal Engineering, Honolulu, Hawaii, July Camp Dresser & Mckee, Inc Study to Revise and Update FEMA s Storm Surge Model. Federal Emergency Management Agency, Washington, D.C.